✦ LIBER ✦

A Short Proof of Guenin's Characterization of Weakly Bipartite Graphs

✍ Scribed by Alexander Schrijver

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 79 KB
Volume: 85
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.2001.2101

No coin nor oath required. For personal study only.

✦ Synopsis

We give a proof of Guenin's theorem characterizing weakly bipartite graphs by not having an odd-K 5 minor. The proof curtails the technical and case-checking parts of Guenin's original proof.

📜 SIMILAR VOLUMES

Proof of a conjecture on cycles in a bip

Proof of a conjecture on cycles in a bipartite graph

✍ Wang, Hong 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 244 KB 👁 2 views

It was conjectured in [Wang, to appear in The Australasian Journal of Combinatorics] that, for each integer k ≥ 2, there exists . This conjecture is also verified for k = 2, 3 in [Wang, to appear; Wang, manuscript]. In this article, we prove this conjecture to be true if n ≥ 3k, i.e., M (k) ≤ 3k. W

A short proof of Kuratowski's graph plan

A short proof of Kuratowski's graph planarity criterion

✍ Makarychev, Yury 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 64 KB 👁 2 views

We present a new short combinatorial proof of the sufficiency part of the well-known Kuratowski's graph planarity criterion. The main steps are to prove that for a minor minimal non-planar graph G and any edge xy: (1) G-x-y does not contain θ-subgraph; (2) G-x-y is homeomorphic to the circle; (3)

Short Solution of Kotzig's Problem for B

Short Solution of Kotzig's Problem for Bipartite Graphs

✍ A.S. Asratian 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 263 KB

In 1975, A. Kotzig posed the following problem: Let G be a t-regular graph which has a proper edge t-coloring, t 4. Is it possible to obtain, from one proper edge t-coloring of G, any other proper edge t-coloring of G using only transformations of 2-colored and 3-colored subgraphs such that the inte

A characterization of weakly four-connec

A characterization of weakly four-connected graphs

✍ Tibor Jordán 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 106 KB

## Abstract A graph __G__ = (__V__, __E__) is called weakly four‐connected if __G__ is 4‐edge‐connected and __G__ − __x__ is 2‐edge‐connected for all __x__ ∈ __V__. We give sufficient conditions for the existence of ‘splittable’ vertices of degree four in weakly four‐connected graphs. By using thes

A short proof of a theorem on Hamiltonia

A short proof of a theorem on Hamiltonian graphs

✍ Ainouche, A. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 219 KB 👁 2 views

In this note, w e give a short proof of a stronger version of the following theorem: Let G be a 2-connected graph of order n such that for any independent set {u, u , w}, then G is hamiltonian. 0 1996 John

A Short Proof of Weyl's Lemma

✍ Roland Lemmert 📂 Article 📅 1988 🏛 John Wiley and Sons 🌐 English ⚖ 71 KB

Let Q c R a be open and LZ~=ZcaD026 be n linear differential opentor with constant coefficients, and adjoint L\*zi = C (l)'"'e,Dazs. We give D proof of the following variant of WEYL'S lemma. d Letit~rta. Every contiwma 8olutim of h = O in the distributional sense is the iocalhj uniform h i t of G+'-